Mr Roy Lichtenstein seems like the odd man out in the story of how 20th-century US art conquered the world. He was not a charismatic, troubled painter, like Mr Jackson Pollock, or an intense, spiritual force of nature such as Mr Mark Rothko, both of whom burnt brightly before snuffing themselves out - Mr Pollock in a car crash after drink-driving in 1956, while Mr Rothko committed suicide in his kitchen in 1970. Neither was Mr Lichtenstein as wilfully insouciant or as instantly recognisable as the shock-headed Mr Andy Warhol, who was almost killed by a bullet in 1968 before succumbing to various ailments after two decades of fame in 1987.

Instead, Mr Lichtenstein became the bridge between two movements - 1950s abstract expressionism and 1960s pop art. Not only did he outlive many of his contemporaries, but he also managed to outlast them stylistically, maintaining his signature dot-matrix painting technique until the very end. "The dots can have a purely decorative meaning," said Mr Lichtenstein of his trademark, "or they can mean an industrial way of extending the colour, or data information, or that the image is a fake."

In London, a new Tate Modern retrospective dedicated to Mr Lichtenstein, the first since his peaceful death in 1997, aims to prove that he was not, however, a one-hit (or a one-dot) wonder. It comprises more than 125 works, ranging from his familiar comic-book frames to huge Chinese-style landscapes, versions of paintings by Mr Piet Mondrian and Mr Claude Monet and some salacious late nudes that were roundly dismissed at the time of their making. The only elements of his oeuvre that aren't represented in the show are the steel sculptures. The exhibition, which has already been seen in Chicago and Washington and will eventually travel to Paris, aims to position Mr Lichtenstein as "one of the great American artists of the 20th century".

Mr Lichtenstein in front of his painting "Whaam!" at Tate Gallery, London, January 1968

Although the vast range of Mr Lichtenstein's production and subject matter goes some way to answering the question as to why we can't simply pin him down as the guy who painted cartoon characters in dots, it doesn't explain why we might still struggle to pick him out of a line-up of great US artists or relate to him as readily as we can his better-known colleagues. The reason is that unlike his headline-grabbing contemporaries, Mr Lichtenstein's rather tame biography can't begin to rival his output as a painter.

Born in 1923 to a Jewish family on the Upper West Side of New York, Mr Lichtenstein grew up intensely serious about art. He devoted himself to his studies and, after being drafted into the US army, returned from war in Europe to teach and practise as an artist. By the mid-1950s he had set up a studio and a family home in Ohio with his two sons and wife, but when the family moved to New Jersey it was his art, rather than his life, that took a dramatic turn.

Mr Lichtenstein's experimentation with images found in his children's books, images of Popeye, Bugs Bunny, Donald Duck and Mickey Mouse (the latter two appearing in what is regarded as his first comic-strip picture, "Look Mickey", in 1961), was, perhaps unsurprisingly, met with critical scorn. While Mr Pollock was featured in a Life magazine spread of 1949 headlined, "Is He the Greatest Living Painter in the United States?", Mr Lichtenstein was profiled by the same publication in 1964 with the headline, "Is He the Worst Artist in the US?"

However, his seemingly rash decision to ditch the gestural spill-and-splatter style of the New York School, in favour of almost mechanically precise renderings of illustrations from magazines, would soon be vindicated. Mr Lichtenstein's lowbrow reference matter, culled from throwaway sources such as newspaper advertisements or pulp-fiction picture books, chimed with the optimism of the new consumerist era and the new pop culture of television. His work, frequently onomatopoeically titled (including "Varoom!", "Whaam!" and "Bratatat"), was every bit as exciting and new as the Action Painting (AKA abstract expressionism) that he'd just metaphorically gunned down.

Mr Lichtenstein soon found a gallery, commercial success and a like-minded group of pop artists to share the limelight with. And yet, after all the accolades, auction records (his highest hammer price, for "Sleeping Girl" of 1964, came in 2012 at just below $45m) and a career that spanned nearly half a century, he's still something of the invisible man of post-war US art. This situation is neatly captured in his 1978 "Self-Portrait", in which Mr Lichtenstein depicts a white T-shirt, with only a blank mirror where his face should be.

But if the artist remains elusive, his work neatly reflects our own desires, whether that is to be the military hero, shooting up enemy planes (in famous panels such as "As I Opened Fire" of 1964) or the object of someone else's romantic affection (as in "Oh, Jeff... I Love You, Too... But" also of 1964). Mr Lichtenstein is hidden behind these characters and remains hard to spot amid his all-over, stencilled dot pattern - the slick surfaces barely register any sign of authorial interference. "I want my painting to look as if it has been programmed," he said in 1967. "I want to hide the record of my hand."

But rather than denigrating himself or his profession, this light touch shows Mr Lichtenstein's humour and humility. As a student, Mr Lichtenstein had aped and copied the works of Mr Pablo Picasso, who he acknowledged as his lifelong artistic hero, not out of spite, but out of begrudging respect: "The things that I have apparently parodied I actually admire and I really don't know what the implication of that is," he said. And, when his own reputation rose and his stock soared, Mr Lichtenstein preferred to half-jokingly paint himself out of the picture, rather than present himself as the all-conquering artistic hero.

That Mr Lichtenstein is not as famous as Mr Warhol, who similarly borrowed from comics and adverts, and hired assistants to paint his pictures for him at much the same time, is not because he was merely a slavish copyist or a graphic arranger - traits that many artists today have latched on to. Rather, it was his decision to put the work in the foreground and let his artistic ego remain the background that ensures his pictures, and not his personality, stand out from the crowd.

Lichtenstein - A Retrospective runs from 21 February to 27 May at Tate Modern, London. tate.org.uk